An analysis of the Covid-19 Pandemic¶

Marco Huang(0201), Jingyun Li(0101)

Introduction¶

COVID-19 is the disease caused by SARS-CoV-2, the coronavirus that emerged in December 2019. COVID-19 can be severe, and has caused millions of deaths around the world as well as lasting health problems in some who have survived the illness. The coronavirus can be spread from person to person. It is diagnosed with a test.

Three years after the break out of the corona virus, the growth of the COVID confirmation rate seems to slow down, providing us with the best timing to examine the pandemic as a whole. Here in part one, we would like to look at COVID in the United States, and several representative states in specific, and discuss what the data illustrates to us. For part two, we're going to look at the relation between confirmation cases and housing prices.

Part 1: About COVID-19¶

1. Data Collection¶

The data collection stage is very important. Without proper data to work with, no analysis can be done. Make sure to find credible and recent data to create accurate models and analysis.

In this project the Covid-19 data we used comes from Johns Hopkins University and is available at this link: https://github.com/CSSEGISandData/COVID-19

1.1 Tool used¶

We used the following tools to collect this data: pandas, numpy, matplotlib, scikit-learn, seaborn, os, folium, and more.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import plotly.express as px
import seaborn
import warnings
import os
import folium
import scipy.stats as stats
from statsmodels.formula.api import ols as o
from sklearn import linear_model
import re
warnings.filterwarnings('ignore')

1.2 Data processing¶

1.2.2 US overall

We want to first look at the overall confirmed and death cases in the US. Here we read the data of the confirmed covid cases throughout the whole world from 1/22/20 till today. For this project, We would focus on the united states.

Below is the global confirmation data. It includes all the countries, their latitude, longitude, and the daily cumulative confirmation among all these countries.

world_conf = pd.read_csv("https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv", sep=',')
world_conf.head()

We first extract the confirmation data for the US from the world data frame. We then calculated the increase of confirmation covid for every day in between and transposed it afterward.

us_conf = pd.melt(world_conf, ['Province/State','Country/Region', 'Lat', 'Long'], var_name="Date", value_name='conf_cases')
us_conf = us_conf.drop(columns=['Province/State', 'Lat', 'Long'])
us_conf = us_conf.rename(columns={'Country/Region': 'Country'})
us_conf["Date"] = pd.to_datetime(us_conf['Date'])
us_conf = us_conf.groupby(['Country', 'Date']).sum()
us_conf["Next_day"] = us_conf['conf_cases'].shift(fill_value=0)
us_conf["conf_change"]= us_conf['conf_cases'] - us_conf['Next_day']
us_conf = us_conf.drop(columns=['Next_day'])
us_conf = us_conf.reset_index()
us_conf = us_conf[us_conf["conf_change"] >= 0] 
us_conf = us_conf[us_conf["Country"]=="US"]
us_conf = us_conf.set_index("Date")
us_conf = us_conf.drop(columns=['Country'])
us_conf.head()

Below is the global death data. It includes all the countries, their latitude, longitude, and the daily cumulative death among all these countries.

world_death = pd.read_csv("https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_global.csv", sep=',')
world_death.head()

We did the same thing for the death data -- we calculated the increase of death cases for every day in between and transposed it afterward.

us_death = pd.melt(world_death, ['Province/State','Country/Region', 'Lat', 'Long'], var_name="Date", value_name='death_cases')
us_death = us_death.drop(columns=['Province/State', 'Lat', 'Long'])
us_death = us_death.rename(columns={'Country/Region': 'Country'})
us_death["Date"] = pd.to_datetime(us_death['Date'])
us_death = us_death.groupby(['Country', 'Date']).sum()
us_death["Next_day"] = us_death['death_cases'].shift(fill_value=0)
us_death["death_change"]= us_death['death_cases'] - us_death['Next_day']
us_death = us_death.drop(columns=['Next_day'])
us_death = us_death.reset_index()
us_death = us_death[us_death["death_change"] >= 0] 
us_death = us_death[us_death["Country"]=="US"]
us_death = us_death.set_index("Date")
us_death = us_death.drop(columns=['Country'])
us_death.head()

We then joined the tables into a data frame us_overall. The new data frame has confirmed cases, daily confirmed the change, death cases, and daily death change data all in one.

us_overall = us_conf.join(us_death, how='outer')
us_overall.head()

1.2.2 US states

Below is the confirmed cases in each state of the United States. Here we would also want to sort out some states that is representative of a certain area. Below is the states we picked for this project, we selected one state for each of the 9 regions.

New England: Maine
Middle Atlantic: New York
East North Central: Wisconsin
West North Central: Kansas
South Atlantic: Maryland
East South Central: Alabama
West South Central: Texas
Mountain: Arizona
Pacific: California

We first read in the data from the Hopkins site.

conf = pd.read_csv("https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_US.csv", sep=',')
conf.head()

We choose 9 state which locate the 9 area of US.

MD = conf[conf["Province_State"] == "Maryland"]
frames = [MD]
confirmed = MD.drop(conf.columns[0:11], axis=1)
confirmed = confirmed.append(confirmed.sum(numeric_only=True), ignore_index=True)
confirmed.drop(confirmed.index[0:26], inplace=True)
list1 = ["Maine", "New York", "Wisconsin", "Kansas", "Alabama", "Texas", "Arizona", "California"]
for x in list1:
  state = conf[conf["Province_State"] == x]
  frames.append(state)
  time = state.drop(state.columns[0:11], axis=1)
  sum = time.append(time.sum(numeric_only=True), ignore_index=True)
  confirmed = confirmed.append(sum.sum(numeric_only=True), ignore_index=True)
confirmed = confirmed.rename(index={0: 'Maryland', 1: 'Maine', 2: 'New York', 3: 'Wisconsin', 4: 'Kansas', 5: 'Alabama', 6: 'Texas', 7: 'Arizona', 8: 'California'})
result = pd.concat(frames)
confirmed = confirmed.swapaxes("index", "columns")
confirmed.index = pd.to_datetime(confirmed.index)
confirmed.head()

Number of deaths by state in the US

us_dead = pd.read_csv("https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_US.csv", sep=',')
us_dead.head()

The totle number of dead in 9 states.

MD2 = us_dead[us_dead["Province_State"] == "Maryland"]
death = MD2.drop(MD2.columns[0:12], axis=1)
death = death.append(death.sum(numeric_only=True), ignore_index=True)
death.drop(death.index[0:26], inplace=True)
for x in list1:
  state2 = us_dead[us_dead["Province_State"] == x]
  time2 = state2.drop(state2.columns[0:12], axis=1)
  sum2 = time2.append(time2.sum(numeric_only=True), ignore_index=True)
  death = death.append(sum2.sum(numeric_only=True), ignore_index=True)
death = death.rename(index={0: 'Maryland', 1: 'Maine', 2: 'New York', 3: 'Wisconsin', 4: 'Kansas', 5: 'Alabama', 6: 'Texas', 7: 'Arizona', 8: 'California'})
death = death.swapaxes("index", "columns")
death.index = pd.to_datetime(death.index)
death.head()

2. Data representation and analysis¶

2.1 Overall trend among all regions in the US¶

2.1.1 Confirmation trend in the US

us_overall.plot(y="conf_cases", legend=None)

<matplotlib.axes._subplots.AxesSubplot at 0x7fe3d69d67f0>

us_overall.plot(y="conf_change")

<matplotlib.axes._subplots.AxesSubplot at 0x7fe3d6707b50>

2.1.2 Deaths trend in the US

us_overall.plot(y="death_cases", legend=None)

<matplotlib.axes._subplots.AxesSubplot at 0x7fe3d69d6640>

us_overall.plot(y="death_change")
# , figsize=(15,10)

<matplotlib.axes._subplots.AxesSubplot at 0x7fe3d6132ee0>

2.2 Trend among all regions in the US¶

confirmed.plot()

<matplotlib.axes._subplots.AxesSubplot at 0x7fe3d607ea30>

Cases in nine states continue to trend upward. It is obvious that the number of confirmed cases in June of 2022 will suddenly increase significantly. One possible reason is that people go on vacation during the summer vacation, which further increases the chance of contact.

death.plot()

<matplotlib.axes._subplots.AxesSubplot at 0x7fe3d5f164f0>

We then did the same thing to the 9 states selected as what we did to the global confirmed and death database-- we calculated the daily increase confirmation rate throught the nine selected states and transposed the dataframe.

result = result.drop(result.columns[[0,1,2,3,4,7,10]], axis=1)
result = pd.melt(result, ['Admin2','Province_State', 'Lat', 'Long_'], var_name="Date", value_name='Cases')
result = result.drop(columns=['Province_State'])
result = result.rename(columns={'Admin2': 'Admin', 'Long_': 'Long'})
result["Date"] = pd.to_datetime(result['Date'])
result = result.groupby(['Admin', 'Date']).sum()
result["Next_day"] = result['Cases'].shift(fill_value=0)
result["Daily_change"]= result['Cases'] - result['Next_day']
result = result.drop(columns=['Next_day'])
result = result.reset_index()
result = result[result["Daily_change"] >= 0]

Afterwards, we put them into the US map and represent the daily increase as a heat map.

result["Date"] = result["Date"].astype(str)
fig = px.scatter_geo(result, lat="Lat", lon="Long",
                     hover_name="Admin", size="Daily_change",size_max=80,
                     animation_frame="Date",
                     scope = "usa",
                     title = "Total Cases")
fig.layout.updatemenus[0].buttons[0].args[1]["frame"]["duration"] = 100
fig.show()

3. Hypothesis testing¶

The mid point of covid is roughly in the middle of June. So we would set that as a middle point and conduct hypothesis testing for the data before the middle of June 2021 and that after.

$H_0$: the mean proportion of death before June 2021 is equal to that after June 2021

$H_\alpha$: the mean proportion of death before June 2021 is greater than that after June 2021

Here is a visualization of the covid death proportion.

us_overall['proportion'] = us_overall.apply(lambda row: row['death_change'] / row['conf_change'], axis=1)
us_overall.plot(y= 'proportion')

<matplotlib.axes._subplots.AxesSubplot at 0x7fe3d61f9700>

us_overall = us_overall.dropna()
us_overall

We then want to extract the proportion data from both time lines.

first = us_overall.head(515)
first

last = us_overall.tail(515)
last

stats.ttest_rel(first["proportion"], last["proportion"])

Ttest_relResult(statistic=14.502805772619178, pvalue=3.3602135329649983e-40)

The result p-value for the paired t-test is roughly 3.36e-40, which is significantly less than the alpha value of 0.05. Therefore we could reject the null hypothesis that the mean proportion of death before June 2021 is equal to that after June 2021.

Part 2: COVID and housing price¶

1. Data Collection¶

New England: Maine
Middle Atlantic: New York
East North Central: Wisconsin
West North Central: Kansas
South Atlantic: Maryland
East South Central: Alabama
West South Central: Texas
Mountain: Arizona
Pacific: California

housing = pd.read_csv("/content/HPI_PO_monthly_hist.csv")
housing.index = pd.to_datetime(housing['Month'])
housing = housing.drop(columns=["Month"])
housing = housing.drop(housing.index[0])
housing.head()

2. Data management/representation + Exploratory data analysis¶

housing.plot(y="USA")

<matplotlib.axes._subplots.AxesSubplot at 0x7fe3f0c62e20>

3. Hypothesis testing¶

first = confirmed[confirmed.index.day == 1]
first = first.drop(first.index[[33, 34,32]])
hypo = pd.concat([housing, first], axis=1)
hypo = hypo.rename(columns={'East North Central': 'East_North','East South Central': 'East_South','Middle Atlantic': 'Middle_Atlantic','New England': 'New_England','South Atlantic': 'South_Atlantic', 'West North Central': 'West_North', 'West South Central': 'West_South', 'New York': 'New_York'})
hypo.head()

import seaborn as sns
hypo_state = ["Maine", "New_York", "Wisconsin", "Kansas", "Maryland", "Alabama", "Texas", "Arizona", "California"]
hpi = ["New_England", "Middle_Atlantic", "East_North", "West_North", "South_Atlantic", "East_South", "West_South", "Mountain", "Pacific"]

#fig, axes = plt.subplots(9, 1, figsize=(10, 50))

for s, h in zip(hypo_state, hpi):
  b = np.array(hypo[s].values)
  a = np.array(hypo[h].values.reshape(-1, 1))
  m = linear_model.LinearRegression().fit(a,b)
  print(("coefficient of " + s + ":"))
  print(str(m.score(a,b)))
  formula = h + " ~ " + s
  result = o(formula = formula, data = hypo).fit()
  print (result.summary())
  plt.plot(a,b,'k.')
  plt.plot(a, m.predict(a))
  plt.show()

coefficient of Maine:
0.864910943785443
                            OLS Regression Results                            
==============================================================================
Dep. Variable:            New_England   R-squared:                       0.865
Model:                            OLS   Adj. R-squared:                  0.860
Method:                 Least Squares   F-statistic:                     192.1
Date:                Fri, 16 Dec 2022   Prob (F-statistic):           1.41e-14
Time:                        12:06:19   Log-Likelihood:                -129.80
No. Observations:                  32   AIC:                             263.6
Df Residuals:                      30   BIC:                             266.5
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    290.2138      3.528     82.250      0.000     283.008     297.420
Maine          0.0002   1.31e-05     13.859      0.000       0.000       0.000
==============================================================================
Omnibus:                        2.406   Durbin-Watson:                   0.119
Prob(Omnibus):                  0.300   Jarque-Bera (JB):                1.269
Skew:                          -0.054   Prob(JB):                        0.530
Kurtosis:                       2.031   Cond. No.                     3.73e+05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.73e+05. This might indicate that there are
strong multicollinearity or other numerical problems.

coefficient of New_York:
0.9242582020415863
                            OLS Regression Results                            
==============================================================================
Dep. Variable:        Middle_Atlantic   R-squared:                       0.924
Model:                            OLS   Adj. R-squared:                  0.922
Method:                 Least Squares   F-statistic:                     366.1
Date:                Fri, 16 Dec 2022   Prob (F-statistic):           2.32e-18
Time:                        12:06:19   Log-Likelihood:                -113.68
No. Observations:                  32   AIC:                             231.4
Df Residuals:                      30   BIC:                             234.3
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    262.3659      2.387    109.909      0.000     257.491     267.241
New_York      7.5e-06   3.92e-07     19.133      0.000     6.7e-06     8.3e-06
==============================================================================
Omnibus:                        6.631   Durbin-Watson:                   0.245
Prob(Omnibus):                  0.036   Jarque-Bera (JB):                2.019
Skew:                          -0.018   Prob(JB):                        0.364
Kurtosis:                       1.770   Cond. No.                     9.43e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 9.43e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

coefficient of Wisconsin:
0.9380086401061278
                            OLS Regression Results                            
==============================================================================
Dep. Variable:             East_North   R-squared:                       0.938
Model:                            OLS   Adj. R-squared:                  0.936
Method:                 Least Squares   F-statistic:                     453.9
Date:                Fri, 16 Dec 2022   Prob (F-statistic):           1.14e-19
Time:                        12:06:19   Log-Likelihood:                -107.87
No. Observations:                  32   AIC:                             219.7
Df Residuals:                      30   BIC:                             222.7
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    243.9571      2.023    120.608      0.000     239.826     248.088
Wisconsin   2.227e-05   1.05e-06     21.306      0.000    2.01e-05    2.44e-05
==============================================================================
Omnibus:                        3.309   Durbin-Watson:                   0.333
Prob(Omnibus):                  0.191   Jarque-Bera (JB):                1.541
Skew:                           0.140   Prob(JB):                        0.463
Kurtosis:                       1.962   Cond. No.                     3.04e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.04e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

coefficient of Kansas:
0.9462160951861599
                            OLS Regression Results                            
==============================================================================
Dep. Variable:             West_North   R-squared:                       0.946
Model:                            OLS   Adj. R-squared:                  0.944
Method:                 Least Squares   F-statistic:                     527.8
Date:                Fri, 16 Dec 2022   Prob (F-statistic):           1.35e-20
Time:                        12:06:20   Log-Likelihood:                -109.99
No. Observations:                  32   AIC:                             224.0
Df Residuals:                      30   BIC:                             226.9
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    290.6082      2.154    134.895      0.000     286.208     295.008
Kansas       5.37e-05   2.34e-06     22.974      0.000    4.89e-05    5.85e-05
==============================================================================
Omnibus:                        2.513   Durbin-Watson:                   0.368
Prob(Omnibus):                  0.285   Jarque-Bera (JB):                1.308
Skew:                           0.080   Prob(JB):                        0.520
Kurtosis:                       2.023   Cond. No.                     1.45e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.45e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

coefficient of Maryland:
0.966012441850216
                            OLS Regression Results                            
==============================================================================
Dep. Variable:         South_Atlantic   R-squared:                       0.966
Model:                            OLS   Adj. R-squared:                  0.965
Method:                 Least Squares   F-statistic:                     852.7
Date:                Fri, 16 Dec 2022   Prob (F-statistic):           1.37e-23
Time:                        12:06:20   Log-Likelihood:                -115.60
No. Observations:                  32   AIC:                             235.2
Df Residuals:                      30   BIC:                             238.1
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    295.0244      2.611    112.997      0.000     289.692     300.357
Maryland       0.0001   4.15e-06     29.201      0.000       0.000       0.000
==============================================================================
Omnibus:                        1.138   Durbin-Watson:                   0.400
Prob(Omnibus):                  0.566   Jarque-Bera (JB):                1.126
Skew:                           0.365   Prob(JB):                        0.569
Kurtosis:                       2.441   Cond. No.                     1.00e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large,  1e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

coefficient of Alabama:
0.9716002661382498
                            OLS Regression Results                            
==============================================================================
Dep. Variable:             East_South   R-squared:                       0.972
Model:                            OLS   Adj. R-squared:                  0.971
Method:                 Least Squares   F-statistic:                     1026.
Date:                Fri, 16 Dec 2022   Prob (F-statistic):           9.23e-25
Time:                        12:06:20   Log-Likelihood:                -105.61
No. Observations:                  32   AIC:                             215.2
Df Residuals:                      30   BIC:                             218.1
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    268.0927      1.916    139.922      0.000     264.180     272.006
Alabama     3.889e-05   1.21e-06     32.037      0.000    3.64e-05    4.14e-05
==============================================================================
Omnibus:                        1.053   Durbin-Watson:                   0.598
Prob(Omnibus):                  0.591   Jarque-Bera (JB):                0.891
Skew:                           0.139   Prob(JB):                        0.640
Kurtosis:                       2.231   Cond. No.                     2.52e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.52e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

coefficient of Texas:
0.9699563858041998
                            OLS Regression Results                            
==============================================================================
Dep. Variable:             West_South   R-squared:                       0.970
Model:                            OLS   Adj. R-squared:                  0.969
Method:                 Least Squares   F-statistic:                     968.5
Date:                Fri, 16 Dec 2022   Prob (F-statistic):           2.15e-24
Time:                        12:06:20   Log-Likelihood:                -107.88
No. Observations:                  32   AIC:                             219.8
Df Residuals:                      30   BIC:                             222.7
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    299.3697      2.055    145.675      0.000     295.173     303.567
Texas       7.722e-06   2.48e-07     31.122      0.000    7.22e-06    8.23e-06
==============================================================================
Omnibus:                        2.863   Durbin-Watson:                   0.567
Prob(Omnibus):                  0.239   Jarque-Bera (JB):                1.415
Skew:                          -0.113   Prob(JB):                        0.493
Kurtosis:                       1.995   Cond. No.                     1.32e+07
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.32e+07. This might indicate that there are
strong multicollinearity or other numerical problems.

coefficient of Arizona:
0.947586025218309
                            OLS Regression Results                            
==============================================================================
Dep. Variable:               Mountain   R-squared:                       0.948
Model:                            OLS   Adj. R-squared:                  0.946
Method:                 Least Squares   F-statistic:                     542.4
Date:                Fri, 16 Dec 2022   Prob (F-statistic):           9.17e-21
Time:                        12:06:20   Log-Likelihood:                -134.47
No. Observations:                  32   AIC:                             272.9
Df Residuals:                      30   BIC:                             275.9
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    408.5110      4.718     86.578      0.000     398.875     418.147
Arizona     4.528e-05   1.94e-06     23.289      0.000    4.13e-05    4.92e-05
==============================================================================
Omnibus:                        0.078   Durbin-Watson:                   0.319
Prob(Omnibus):                  0.962   Jarque-Bera (JB):                0.295
Skew:                          -0.020   Prob(JB):                        0.863
Kurtosis:                       2.532   Cond. No.                     3.88e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.88e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

coefficient of California:
0.8944032883329911
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                Pacific   R-squared:                       0.894
Model:                            OLS   Adj. R-squared:                  0.891
Method:                 Least Squares   F-statistic:                     254.1
Date:                Fri, 16 Dec 2022   Prob (F-statistic):           3.44e-16
Time:                        12:06:20   Log-Likelihood:                -132.95
No. Observations:                  32   AIC:                             269.9
Df Residuals:                      30   BIC:                             272.8
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    345.7579      4.357     79.362      0.000     336.860     354.656
California  6.247e-06   3.92e-07     15.941      0.000    5.45e-06    7.05e-06
==============================================================================
Omnibus:                        0.409   Durbin-Watson:                   0.229
Prob(Omnibus):                  0.815   Jarque-Bera (JB):                0.552
Skew:                          -0.076   Prob(JB):                        0.759
Kurtosis:                       2.375   Cond. No.                     1.72e+07
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.72e+07. This might indicate that there are
strong multicollinearity or other numerical problems.

We can see that the coefficient for 9 states are all greater than 0.7, which tell us that the change in House Price Index (HPI) and number of confirmed in each state has strong relationship.

For the Maine. The $R^2$ is 0.865. So, 86.5% of the HPI can explain by the # comfirmed. The p-value of the Intercept in very low(lower than default $\alpha$ 0.05) which indecates that Intercept in significant in the model. We should keep $\beta_0$ value in the equation.

The p-value of the # comfirmed in Maine in low(lower than default $\alpha$ 0.05) which indecates that number of confirmed is significant in the model and we should keep $\beta_1$ value in the equation.

Assumption: The data is a random sample from the normal distribution. Based on the plot there is linear relationship. The dependent variable is continuous variable.

Base on the information above, the model is reliable and can be used.

5. Insights attained¶

Motivation: each tutorial should be sufficiently motivated. If there is not motivation for the analysis, why would we ‘do data science’ on this topic?

Understanding: the reader of the tutorial should walk away with some new understanding of the topic at hand. If it’s not possible for a reader to state ‘what they learned’ from reading your tutorial, then why do the analysis?

Resources: tutorials should help the reader learn a skill, but they should also provide a launching pad for the reader to further develop that skill. The tutorial should link to additional resources wherever appropriate, so that a well-motivated reader can read further on techniques that have been used in the tutorial.

Prose: it’s very easy to write the literal English for what the Python code is doing, but that’s not very useful. The prose should enhance, the tutorial, adding additional context and insight.

Code: code should be clear and commented. Function definitions should be described and given context/motivation. If the prose helps the reader understand why you’ve written the code, the comments in the code should be sufficient for the reader to learn how.

Pipeline: all stages of the pipeline should be discussed. We will be looking for ‘good science’, with discussion of each stage and what it’s implications/consequences are.

Communication of Approach: every technical choice has alternatives, why did you choose the approach taken in the tutorial? A reader should walk away with some idea of what the trade-offs may be.

Formatting and Subjective Evaluation: does the tutorial seem polished and ‘publishable’, or haphazard and quickly thrown together? The tutorials should read as well put-together and having undergone a few iterations of editing and refinement. This should be the easiest of the dimensions.

# To HTML:
# !jupyter nbconvert --to html /content/CMSC320_Final.ipynb

	Province/State	Country/Region	Lat	Long	...	12/6/22	12/7/22	12/8/22	12/9/22	12/10/22	12/11/22	12/12/22	12/13/22	12/14/22	12/15/22
0	NaN	Afghanistan	33.93911	67.709953	...	206331	206414	206465	206504	206543	206603	206702	206743	206788	206879
1	NaN	Albania	41.15330	20.168300	...	333455	333472	333490	333491	333521	333533	333535	333567	333591	333613
2	NaN	Algeria	28.03390	1.659600	...	271122	271128	271135	271140	271146	271146	271147	271149	271156	271156
3	NaN	Andorra	42.50630	1.521800	...	47219	47446	47446	47446	47446	47446	47446	47446	47606	47606
4	NaN	Angola	-11.20270	17.873900	...	104750	104808	104808	104808	104808	104808	104808	104808	104946	104946

	conf_cases	conf_change
Date
2020-01-23	1	0
2020-01-24	2	1
2020-01-25	2	0
2020-01-26	5	3
2020-01-27	5	0

	Province/State	Country/Region	Lat	Long	...	12/6/22	12/7/22	12/8/22	12/9/22	12/10/22	12/11/22	12/12/22	12/13/22	12/14/22	12/15/22
0	NaN	Afghanistan	33.93911	67.709953	...	7835	7837	7839	7839	7839	7839	7840	7843	7843	7843
1	NaN	Albania	41.15330	20.168300	...	3594	3594	3594	3594	3594	3594	3594	3594	3594	3594
2	NaN	Algeria	28.03390	1.659600	...	6881	6881	6881	6881	6881	6881	6881	6881	6881	6881
3	NaN	Andorra	42.50630	1.521800	...	157	158	158	158	158	158	158	158	158	158
4	NaN	Angola	-11.20270	17.873900	...	1925	1925	1925	1925	1925	1925	1925	1925	1928	1928

	death_cases	death_change
Date
2020-01-22	0	0
2020-01-23	0	0
2020-01-24	0	0
2020-01-25	0	0
2020-01-26	0	0

	UID	iso2	iso3	code3	FIPS	Admin2	Province_State	Country_Region	Lat	Long_	...	12/6/22	12/7/22	12/8/22	12/9/22	12/10/22	12/11/22	12/12/22	12/13/22	12/14/22	12/15/22
0	84001001	US	USA	840	1001.0	Autauga	Alabama	US	32.539527	-86.644082	...	18680	18752	18752	18752	18752	18752	18752	18752	18847	18847
1	84001003	US	USA	840	1003.0	Baldwin	Alabama	US	30.727750	-87.722071	...	66730	66951	66951	66951	66951	66951	66951	66951	67221	67221
2	84001005	US	USA	840	1005.0	Barbour	Alabama	US	31.868263	-85.387129	...	6980	6989	6989	6989	6989	6989	6989	6989	7007	7007
3	84001007	US	USA	840	1007.0	Bibb	Alabama	US	32.996421	-87.125115	...	7637	7653	7653	7653	7653	7653	7653	7653	7668	7668
4	84001009	US	USA	840	1009.0	Blount	Alabama	US	33.982109	-86.567906	...	17500	17559	17559	17559	17559	17559	17559	17559	17648	17648

	conf_cases	conf_change	death_cases	death_change	proportion
Date
2020-01-24	2.0	1.0	0.0	0.0	0.000000
2020-01-26	5.0	3.0	0.0	0.0	0.000000
2020-01-29	6.0	1.0	0.0	0.0	0.000000
2020-01-31	8.0	2.0	0.0	0.0	0.000000
2020-02-03	11.0	3.0	0.0	0.0	0.000000
...	...	...	...	...	...
2022-12-11	99422778.0	4939.0	1084601.0	0.0	0.000000
2022-12-12	99479472.0	56694.0	1084813.0	212.0	0.003739
2022-12-13	99570282.0	90810.0	1085386.0	573.0	0.006310
2022-12-14	99716762.0	146480.0	1086302.0	916.0	0.006253
2022-12-15	99826698.0	109936.0	1087013.0	711.0	0.006467

	conf_cases	conf_change	death_cases	death_change	proportion
Date
2021-07-17	34187224.0	14066.0	605092.0	72.0	0.005119
2021-07-18	34207594.0	20370.0	605187.0	95.0	0.004664
2021-07-19	34256821.0	49227.0	605385.0	198.0	0.004022
2021-07-20	34296710.0	39889.0	605675.0	290.0	0.007270
2021-07-21	34344582.0	47872.0	606038.0	363.0	0.007583
...	...	...	...	...	...
2022-12-11	99422778.0	4939.0	1084601.0	0.0	0.000000
2022-12-12	99479472.0	56694.0	1084813.0	212.0	0.003739
2022-12-13	99570282.0	90810.0	1085386.0	573.0	0.006310
2022-12-14	99716762.0	146480.0	1086302.0	916.0	0.006253
2022-12-15	99826698.0	109936.0	1087013.0	711.0	0.006467

	East North Central	East South Central	Middle Atlantic	Mountain	New England	Pacific	South Atlantic	West North Central	West South Central	USA
Month
2020-02-01	232.67	260.54	249.97	392.87	264.70	327.64	289.09	278.23	291.92	282.50
2020-03-01	235.97	262.93	251.29	397.67	268.38	331.57	290.31	281.34	294.82	285.24
2020-04-01	238.33	265.19	253.43	399.73	270.87	334.22	292.29	284.73	296.96	287.59
2020-05-01	239.57	266.47	255.06	399.92	269.87	332.23	293.87	285.82	297.94	288.36
2020-06-01	243.02	269.12	256.54	404.90	274.06	336.72	296.63	289.66	303.16	291.92